[libc-commits] [libc] [libc][math] Implement powf function correctly rounded to all rounding modes. (PR #71188)
via libc-commits
libc-commits at lists.llvm.org
Fri Nov 3 07:34:21 PDT 2023
llvmbot wrote:
<!--LLVM PR SUMMARY COMMENT-->
@llvm/pr-subscribers-libc
Author: None (lntue)
<details>
<summary>Changes</summary>
We compute `pow(x, y)` using the formula
```
pow(x, y) = x^y = 2^(y * log2(x))
```
We follow similar steps as in `log2f(x)` and `exp2f(x)`, by breaking down into `hi + mid + lo` parts, in which `hi` parts are computed using the exponent field directly, `mid` parts will use look-up tables, and `lo` parts are approximated by polynomials.
We add some speedup for common use-cases:
```
pow(2, y) = exp2(y)
pow(10, y) = exp10(y)
pow(x, 2) = x * x
pow(x, 1/2) = sqrt(x)
pow(x, -1/2) = rsqrt(x) - to be added
```
---
Patch is 71.90 KiB, truncated to 20.00 KiB below, full version: https://github.com/llvm/llvm-project/pull/71188.diff
19 Files Affected:
- (modified) libc/config/darwin/arm/entrypoints.txt (+1)
- (modified) libc/config/linux/aarch64/entrypoints.txt (+1)
- (modified) libc/config/linux/riscv/entrypoints.txt (+1)
- (modified) libc/config/linux/x86_64/entrypoints.txt (+1)
- (modified) libc/config/windows/entrypoints.txt (+1)
- (modified) libc/docs/math/index.rst (+2-1)
- (modified) libc/spec/stdc.td (+1)
- (modified) libc/src/math/generic/CMakeLists.txt (+30)
- (modified) libc/src/math/generic/common_constants.cpp (+87)
- (modified) libc/src/math/generic/common_constants.h (+5)
- (modified) libc/src/math/generic/log2f.cpp (-46)
- (added) libc/src/math/generic/powf.cpp (+840)
- (modified) libc/test/UnitTest/FPMatcher.h (+7)
- (modified) libc/test/src/math/CMakeLists.txt (+13)
- (added) libc/test/src/math/powf_test.cpp (+123)
- (modified) libc/test/src/math/smoke/CMakeLists.txt (+12)
- (added) libc/test/src/math/smoke/powf_test.cpp (+189)
- (modified) libc/utils/MPFRWrapper/MPFRUtils.cpp (+8)
- (modified) libc/utils/MPFRWrapper/MPFRUtils.h (+1)
``````````diff
diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
index ecdd2d0624fcf5d..362138c92a6869f 100644
--- a/libc/config/darwin/arm/entrypoints.txt
+++ b/libc/config/darwin/arm/entrypoints.txt
@@ -199,6 +199,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
index 52e9e8036a3fae3..096e2afb06e5a9d 100644
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -316,6 +316,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/config/linux/riscv/entrypoints.txt b/libc/config/linux/riscv/entrypoints.txt
index 52ca12121812d12..7dadbc7f8285477 100644
--- a/libc/config/linux/riscv/entrypoints.txt
+++ b/libc/config/linux/riscv/entrypoints.txt
@@ -325,6 +325,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
index ab105e1d6344725..31ea282edb59126 100644
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -329,6 +329,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
index 1ee088e399438b7..5611b399e8bca8b 100644
--- a/libc/config/windows/entrypoints.txt
+++ b/libc/config/windows/entrypoints.txt
@@ -198,6 +198,7 @@ set(TARGET_LIBM_ENTRYPOINTS
libc.src.math.nextafter
libc.src.math.nextafterf
libc.src.math.nextafterl
+ libc.src.math.powf
libc.src.math.remainderf
libc.src.math.remainder
libc.src.math.remainderl
diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
index 77b3c8b99a0c2bc..7c83691c0d9c801 100644
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -420,7 +420,7 @@ Higher Math Functions
+------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
| pow | | | | | | | | | | | | |
+------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| powf | | | | | | | | | | | | |
+| powf | |check| | |check| | | |check| | |check| | | | |check| | | | | |
+------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
| powl | | | | | | | | | | | | |
+------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
@@ -493,6 +493,7 @@ log |check| |check|
log10 |check| |check|
log1p |check| |check|
log2 |check| |check|
+pow |check|
sin |check| large
sincos |check| large
sinh |check|
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
index 1e9043b841ff1d8..239d8f9843cfc0f 100644
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -491,6 +491,7 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"nextafter", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
FunctionSpec<"nextafterl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>]>,
+ FunctionSpec<"powf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
FunctionSpec<"pow", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
FunctionSpec<"coshf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 843349ccdc196a7..8fc2b0850fbc077 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -747,6 +747,36 @@ add_entrypoint_object(
-O3
)
+add_entrypoint_object(
+ powf
+ SRCS
+ powf.cpp
+ HDRS
+ ../powf.h
+ DEPENDS
+ .common_constants
+ .explogxf
+ .exp2f
+ .exp10f
+ libc.src.__support.builtin_wrappers
+ libc.src.__support.CPP.bit
+ libc.src.__support.CPP.optional
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.nearest_integer
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.rounding_mode
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.FPUtil.triple_double
+ libc.src.__support.macros.optimization
+ libc.include.errno
+ libc.src.errno.errno
+ libc.include.math
+ COMPILE_OPTIONS
+ -O3
+)
+
add_entrypoint_object(
copysign
SRCS
diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
index 737d2ab77121adb..1a23d00297105f7 100644
--- a/libc/src/math/generic/common_constants.cpp
+++ b/libc/src/math/generic/common_constants.cpp
@@ -227,6 +227,51 @@ alignas(64) const double LOG_R[128] = {
0x1.5707a26bb8c66p-1, 0x1.5af405c3649ep-1, 0x1.5af405c3649ep-1,
0x1.5ee82aa24192p-1, 0x0.000000000000p0};
+alignas(64) const double LOG2_R[128] = {
+ 0x0.0000000000000p+0, 0x1.72c7ba20f7327p-7, 0x1.743ee861f3556p-6,
+ 0x1.184b8e4c56af8p-5, 0x1.77394c9d958d5p-5, 0x1.d6ebd1f1febfep-5,
+ 0x1.1bb32a600549dp-4, 0x1.4c560fe68af88p-4, 0x1.7d60496cfbb4cp-4,
+ 0x1.960caf9abb7cap-4, 0x1.c7b528b70f1c5p-4, 0x1.f9c95dc1d1165p-4,
+ 0x1.097e38ce60649p-3, 0x1.22dadc2ab3497p-3, 0x1.3c6fb650cde51p-3,
+ 0x1.494f863b8df35p-3, 0x1.633a8bf437ce1p-3, 0x1.7046031c79f85p-3,
+ 0x1.8a8980abfbd32p-3, 0x1.97c1cb13c7ec1p-3, 0x1.b2602497d5346p-3,
+ 0x1.bfc67a7fff4ccp-3, 0x1.dac22d3e441d3p-3, 0x1.e857d3d361368p-3,
+ 0x1.01d9bbcfa61d4p-2, 0x1.08bce0d95fa38p-2, 0x1.169c05363f158p-2,
+ 0x1.1d982c9d52708p-2, 0x1.249cd2b13cd6cp-2, 0x1.32bfee370ee68p-2,
+ 0x1.39de8e1559f6fp-2, 0x1.4106017c3eca3p-2, 0x1.4f6fbb2cec598p-2,
+ 0x1.56b22e6b578e5p-2, 0x1.5dfdcf1eeae0ep-2, 0x1.6552b49986277p-2,
+ 0x1.6cb0f6865c8eap-2, 0x1.7b89f02cf2aadp-2, 0x1.8304d90c11fd3p-2,
+ 0x1.8a8980abfbd32p-2, 0x1.921800924dd3bp-2, 0x1.99b072a96c6b2p-2,
+ 0x1.a8ff971810a5ep-2, 0x1.b0b67f4f4681p-2, 0x1.b877c57b1b07p-2,
+ 0x1.c043859e2fdb3p-2, 0x1.c819dc2d45fe4p-2, 0x1.cffae611ad12bp-2,
+ 0x1.d7e6c0abc3579p-2, 0x1.dfdd89d586e2bp-2, 0x1.e7df5fe538ab3p-2,
+ 0x1.efec61b011f85p-2, 0x1.f804ae8d0cd02p-2, 0x1.0014332be0033p-1,
+ 0x1.042bd4b9a7c99p-1, 0x1.08494c66b8efp-1, 0x1.0c6caaf0c5597p-1,
+ 0x1.1096015dee4dap-1, 0x1.14c560fe68af9p-1, 0x1.18fadb6e2d3c2p-1,
+ 0x1.1d368296b5255p-1, 0x1.217868b0c37e8p-1, 0x1.25c0a0463bebp-1,
+ 0x1.2a0f3c340705cp-1, 0x1.2e644fac04fd8p-1, 0x1.2e644fac04fd8p-1,
+ 0x1.32bfee370ee68p-1, 0x1.37222bb70747cp-1, 0x1.3b8b1c68fa6edp-1,
+ 0x1.3ffad4e74f1d6p-1, 0x1.44716a2c08262p-1, 0x1.44716a2c08262p-1,
+ 0x1.48eef19317991p-1, 0x1.4d7380dcc422dp-1, 0x1.51ff2e30214bcp-1,
+ 0x1.5692101d9b4a6p-1, 0x1.5b2c3da19723bp-1, 0x1.5b2c3da19723bp-1,
+ 0x1.5fcdce2727ddbp-1, 0x1.6476d98ad990ap-1, 0x1.6927781d932a8p-1,
+ 0x1.6927781d932a8p-1, 0x1.6ddfc2a78fc63p-1, 0x1.729fd26b707c8p-1,
+ 0x1.7767c12967a45p-1, 0x1.7767c12967a45p-1, 0x1.7c37a9227e7fbp-1,
+ 0x1.810fa51bf65fdp-1, 0x1.810fa51bf65fdp-1, 0x1.85efd062c656dp-1,
+ 0x1.8ad846cf369a4p-1, 0x1.8ad846cf369a4p-1, 0x1.8fc924c89ac84p-1,
+ 0x1.94c287492c4dbp-1, 0x1.94c287492c4dbp-1, 0x1.99c48be2063c8p-1,
+ 0x1.9ecf50bf43f13p-1, 0x1.9ecf50bf43f13p-1, 0x1.a3e2f4ac43f6p-1,
+ 0x1.a8ff971810a5ep-1, 0x1.a8ff971810a5ep-1, 0x1.ae255819f022dp-1,
+ 0x1.b35458761d479p-1, 0x1.b35458761d479p-1, 0x1.b88cb9a2ab521p-1,
+ 0x1.b88cb9a2ab521p-1, 0x1.bdce9dcc96187p-1, 0x1.c31a27dd00b4ap-1,
+ 0x1.c31a27dd00b4ap-1, 0x1.c86f7b7ea4a89p-1, 0x1.c86f7b7ea4a89p-1,
+ 0x1.cdcebd2373995p-1, 0x1.d338120a6dd9dp-1, 0x1.d338120a6dd9dp-1,
+ 0x1.d8aba045b01c8p-1, 0x1.d8aba045b01c8p-1, 0x1.de298ec0bac0dp-1,
+ 0x1.de298ec0bac0dp-1, 0x1.e3b20546f554ap-1, 0x1.e3b20546f554ap-1,
+ 0x1.e9452c8a71028p-1, 0x1.e9452c8a71028p-1, 0x1.eee32e2aeccbfp-1,
+ 0x1.eee32e2aeccbfp-1, 0x1.f48c34bd1e96fp-1, 0x1.f48c34bd1e96fp-1,
+ 0x1.fa406bd2443dfp-1, 0x1.0000000000000p0};
+
// Generated by Sollya with:
// for i from 0 to 127 do {
// r = 2^-8 * ceil( 2^8 * (1 - 2^(-8)) / (1 + i*2^-7) );
@@ -395,6 +440,48 @@ alignas(64) const int S2[193] = {
-0x1cd, -0x1d1, -0x1d5, -0x1d9, -0x1dd, -0x1e0, -0x1e4, -0x1e8, -0x1ec,
-0x1f0, -0x1f4, -0x1f8, -0x1fc};
+alignas(64) const double R2[193] = {
+ 0x1.0101p0, 0x1.00fdp0, 0x1.00f9p0, 0x1.00f5p0, 0x1.00f1p0,
+ 0x1.00edp0, 0x1.00e9p0, 0x1.00e5p0, 0x1.00e1p0, 0x1.00ddp0,
+ 0x1.00d9p0, 0x1.00d5p0, 0x1.00d1p0, 0x1.00cdp0, 0x1.00c9p0,
+ 0x1.00c5p0, 0x1.00c1p0, 0x1.00bdp0, 0x1.00b9p0, 0x1.00b4p0,
+ 0x1.00bp0, 0x1.00acp0, 0x1.00a8p0, 0x1.00a4p0, 0x1.00ap0,
+ 0x1.009cp0, 0x1.0098p0, 0x1.0094p0, 0x1.009p0, 0x1.008cp0,
+ 0x1.0088p0, 0x1.0084p0, 0x1.008p0, 0x1.007cp0, 0x1.0078p0,
+ 0x1.0074p0, 0x1.007p0, 0x1.006cp0, 0x1.0068p0, 0x1.0064p0,
+ 0x1.006p0, 0x1.005cp0, 0x1.0058p0, 0x1.0054p0, 0x1.005p0,
+ 0x1.004cp0, 0x1.0048p0, 0x1.0044p0, 0x1.004p0, 0x1.003cp0,
+ 0x1.0038p0, 0x1.0034p0, 0x1.003p0, 0x1.002cp0, 0x1.0028p0,
+ 0x1.0024p0, 0x1.002p0, 0x1.001cp0, 0x1.0018p0, 0x1.0014p0,
+ 0x1.001p0, 0x1.000cp0, 0x1.0008p0, 0x1.0004p0, 0x1p0,
+ 0x1.fff8p-1, 0x1.fffp-1, 0x1.ffe8p-1, 0x1.ffep-1, 0x1.ffd8p-1,
+ 0x1.ffdp-1, 0x1.ffc8p-1, 0x1.ffcp-1, 0x1.ffb8p-1, 0x1.ffbp-1,
+ 0x1.ffa8p-1, 0x1.ffap-1, 0x1.ff98p-1, 0x1.ff9p-1, 0x1.ff88p-1,
+ 0x1.ff8p-1, 0x1.ff78p-1, 0x1.ff7p-1, 0x1.ff68p-1, 0x1.ff6p-1,
+ 0x1.ff58p-1, 0x1.ff5p-1, 0x1.ff48p-1, 0x1.ff4p-1, 0x1.ff38p-1,
+ 0x1.ff3p-1, 0x1.ff28p-1, 0x1.ff2p-1, 0x1.ff18p-1, 0x1.ff1p-1,
+ 0x1.ff08p-1, 0x1.ffp-1, 0x1.fef8p-1, 0x1.fefp-1, 0x1.fee8p-1,
+ 0x1.feep-1, 0x1.fed8p-1, 0x1.fedp-1, 0x1.fec8p-1, 0x1.fecp-1,
+ 0x1.feb8p-1, 0x1.febp-1, 0x1.fea8p-1, 0x1.feap-1, 0x1.fe98p-1,
+ 0x1.fe92p-1, 0x1.fe8ap-1, 0x1.fe82p-1, 0x1.fe7ap-1, 0x1.fe72p-1,
+ 0x1.fe6ap-1, 0x1.fe62p-1, 0x1.fe5ap-1, 0x1.fe52p-1, 0x1.fe4ap-1,
+ 0x1.fe42p-1, 0x1.fe3ap-1, 0x1.fe32p-1, 0x1.fe2ap-1, 0x1.fe22p-1,
+ 0x1.fe1ap-1, 0x1.fe12p-1, 0x1.fe0ap-1, 0x1.fe02p-1, 0x1.fdfap-1,
+ 0x1.fdf2p-1, 0x1.fdeap-1, 0x1.fde2p-1, 0x1.fddap-1, 0x1.fdd2p-1,
+ 0x1.fdcap-1, 0x1.fdc2p-1, 0x1.fdbap-1, 0x1.fdb2p-1, 0x1.fdaap-1,
+ 0x1.fda2p-1, 0x1.fd9ap-1, 0x1.fd92p-1, 0x1.fd8cp-1, 0x1.fd84p-1,
+ 0x1.fd7cp-1, 0x1.fd74p-1, 0x1.fd6cp-1, 0x1.fd64p-1, 0x1.fd5cp-1,
+ 0x1.fd54p-1, 0x1.fd4cp-1, 0x1.fd44p-1, 0x1.fd3cp-1, 0x1.fd34p-1,
+ 0x1.fd2cp-1, 0x1.fd24p-1, 0x1.fd1cp-1, 0x1.fd14p-1, 0x1.fd0cp-1,
+ 0x1.fd04p-1, 0x1.fcfcp-1, 0x1.fcf4p-1, 0x1.fcecp-1, 0x1.fce4p-1,
+ 0x1.fcdcp-1, 0x1.fcd6p-1, 0x1.fccep-1, 0x1.fcc6p-1, 0x1.fcbep-1,
+ 0x1.fcb6p-1, 0x1.fcaep-1, 0x1.fca6p-1, 0x1.fc9ep-1, 0x1.fc96p-1,
+ 0x1.fc8ep-1, 0x1.fc86p-1, 0x1.fc7ep-1, 0x1.fc76p-1, 0x1.fc6ep-1,
+ 0x1.fc66p-1, 0x1.fc5ep-1, 0x1.fc56p-1, 0x1.fc4ep-1, 0x1.fc46p-1,
+ 0x1.fc4p-1, 0x1.fc38p-1, 0x1.fc3p-1, 0x1.fc28p-1, 0x1.fc2p-1,
+ 0x1.fc18p-1, 0x1.fc1p-1, 0x1.fc08p-1,
+};
+
// Logarithm range reduction - Step 3:
// r(k) = 2^-21 round(2^21 / (1 + k*2^-21)) for k = -80 .. 80.
// Output range:
diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h
index df9d7828bf1609d..13fc8d757cb8ca3 100644
--- a/libc/src/math/generic/common_constants.h
+++ b/libc/src/math/generic/common_constants.h
@@ -34,6 +34,9 @@ extern const double CD[128];
extern const double LOG_R[128];
extern const NumberPair<double> LOG_R_DD[128];
+// Lookup table for -log2(r)
+extern const double LOG2_R[128];
+
// Minimax polynomial for (log(1 + x) - x)/x^2, generated by sollya with:
// > P = fpminimax((log(1 + x) - x)/x^2, 5, [|D...|], [-2^-8, 2^-7]);
constexpr double LOG_COEFFS[6] = {-0x1.fffffffffffffp-2, 0x1.5555555554a9bp-2,
@@ -45,6 +48,8 @@ extern const int S2[193];
extern const int S3[161];
extern const int S4[130];
+extern const double R2[193];
+
// log(2) generated by Sollya with:
// > a = 2^-43 * nearestint(2^43*log(2));
// LSB = 2^-43 is chosen so that e_x * LOG_2_HI is exact for -1075 < e_x < 1024.
diff --git a/libc/src/math/generic/log2f.cpp b/libc/src/math/generic/log2f.cpp
index cbb71fb91b10705..7665a90f092359f 100644
--- a/libc/src/math/generic/log2f.cpp
+++ b/libc/src/math/generic/log2f.cpp
@@ -53,52 +53,6 @@
namespace LIBC_NAMESPACE {
-// Lookup table for log2(f) = log2(1 + n*2^(-7)) where n = 0..127.
-static constexpr double LOG2_R[128] = {
- 0x0.0000000000000p+0, 0x1.72c7ba20f7327p-7, 0x1.743ee861f3556p-6,
- 0x1.184b8e4c56af8p-5, 0x1.77394c9d958d5p-5, 0x1.d6ebd1f1febfep-5,
- 0x1.1bb32a600549dp-4, 0x1.4c560fe68af88p-4, 0x1.7d60496cfbb4cp-4,
- 0x1.960caf9abb7cap-4, 0x1.c7b528b70f1c5p-4, 0x1.f9c95dc1d1165p-4,
- 0x1.097e38ce60649p-3, 0x1.22dadc2ab3497p-3, 0x1.3c6fb650cde51p-3,
- 0x1.494f863b8df35p-3, 0x1.633a8bf437ce1p-3, 0x1.7046031c79f85p-3,
- 0x1.8a8980abfbd32p-3, 0x1.97c1cb13c7ec1p-3, 0x1.b2602497d5346p-3,
- 0x1.bfc67a7fff4ccp-3, 0x1.dac22d3e441d3p-3, 0x1.e857d3d361368p-3,
- 0x1.01d9bbcfa61d4p-2, 0x1.08bce0d95fa38p-2, 0x1.169c05363f158p-2,
- 0x1.1d982c9d52708p-2, 0x1.249cd2b13cd6cp-2, 0x1.32bfee370ee68p-2,
- 0x1.39de8e1559f6fp-2, 0x1.4106017c3eca3p-2, 0x1.4f6fbb2cec598p-2,
- 0x1.56b22e6b578e5p-2, 0x1.5dfdcf1eeae0ep-2, 0x1.6552b49986277p-2,
- 0x1.6cb0f6865c8eap-2, 0x1.7b89f02cf2aadp-2, 0x1.8304d90c11fd3p-2,
- 0x1.8a8980abfbd32p-2, 0x1.921800924dd3bp-2, 0x1.99b072a96c6b2p-2,
- 0x1.a8ff971810a5ep-2, 0x1.b0b67f4f4681p-2, 0x1.b877c57b1b07p-2,
- 0x1.c043859e2fdb3p-2, 0x1.c819dc2d45fe4p-2, 0x1.cffae611ad12bp-2,
- 0x1.d7e6c0abc3579p-2, 0x1.dfdd89d586e2bp-2, 0x1.e7df5fe538ab3p-2,
- 0x1.efec61b011f85p-2, 0x1.f804ae8d0cd02p-2, 0x1.0014332be0033p-1,
- 0x1.042bd4b9a7c99p-1, 0x1.08494c66b8efp-1, 0x1.0c6caaf0c5597p-1,
- 0x1.1096015dee4dap-1, 0x1.14c560fe68af9p-1, 0x1.18fadb6e2d3c2p-1,
- 0x1.1d368296b5255p-1, 0x1.217868b0c37e8p-1, 0x1.25c0a0463bebp-1,
- 0x1.2a0f3c340705cp-1, 0x1.2e644fac04fd8p-1, 0x1.2e644fac04fd8p-1,
- 0x1.32bfee370ee68p-1, 0x1.37222bb70747cp-1, 0x1.3b8b1c68fa6edp-1,
- 0x1.3ffad4e74f1d6p-1, 0x1.44716a2c08262p-1, 0x1.44716a2c08262p-1,
- 0x1.48eef19317991p-1, 0x1.4d7380dcc422dp-1, 0x1.51ff2e30214bcp-1,
- 0x1.5692101d9b4a6p-1, 0x1.5b2c3da19723bp-1, 0x1.5b2c3da19723bp-1,
- 0x1.5fcdce2727ddbp-1, 0x1.6476d98ad990ap-1, 0x1.6927781d932a8p-1,
- 0x1.6927781d932a8p-1, 0x1.6ddfc2a78fc63p-1, 0x1.729fd26b707c8p-1,
- 0x1.7767c12967a45p-1, 0x1.7767c12967a45p-1, 0x1.7c37a9227e7fbp-1,
- 0x1.810fa51bf65fdp-1, 0x1.810fa51bf65fdp-1, 0x1.85efd062c656dp-1,
- 0x1.8ad846cf369a4p-1, 0x1.8ad846cf369a4p-1, 0x1.8fc924c89ac84p-1,
- 0x1.94c287492c4dbp-1, 0x1.94c287492c4dbp-1, 0x1.99c48be2063c8p-1,
- 0x1.9ecf50bf43f13p-1, 0x1.9ecf50bf43f13p-1, 0x1.a3e2f4ac43f6p-1,
- 0x1.a8ff971810a5ep-1, 0x1.a8ff971810a5ep-1, 0x1.ae255819f022dp-1,
- 0x1.b35458761d479p-1, 0x1.b35458761d479p-1, 0x1.b88cb9a2ab521p-1,
- 0x1.b88cb9a2ab521p-1, 0x1.bdce9dcc96187p-1, 0x1.c31a27dd00b4ap-1,
- 0x1.c31a27dd00b4ap-1, 0x1.c86f7b7ea4a89p-1, 0x1.c86f7b7ea4a89p-1,
- 0x1.cdcebd2373995p-1, 0x1.d338120a6dd9dp-1, 0x1.d338120a6dd9dp-1,
- 0x1.d8aba045b01c8p-1, 0x1.d8aba045b01c8p-1, 0x1.de298ec0bac0dp-1,
- 0x1.de298ec0bac0dp-1, 0x1.e3b20546f554ap-1, 0x1.e3b20546f554ap-1,
- 0x1.e9452c8a71028p-1, 0x1.e9452c8a71028p-1, 0x1.eee32e2aeccbfp-1,
- 0x1.eee32e2aeccbfp-1, 0x1.f48c34bd1e96fp-1, 0x1.f48c34bd1e96fp-1,
- 0x1.fa406bd2443dfp-1, 0x1.0000000000000p0};
-
LLVM_LIBC_FUNCTION(float, log2f, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
diff --git a/libc/src/math/generic/powf.cpp b/libc/src/math/generic/powf.cpp
new file mode 100644
index 000000000000000..c432a4fa372f24b
--- /dev/null
+++ b/libc/src/math/generic/powf.cpp
@@ -0,0 +1,840 @@
+//===-- Single-precision x^y function -------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/powf.h"
+#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/optional.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/builtin_wrappers.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/math/exp10f.h"
+#include "src/math/exp2f.h"
+
+#include <errno.h>
+
+namespace LIBC_NAMESPACE {
+
+using fputil::DoubleDouble;
+using fputil::TripleDouble;
+
+namespace {
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+constexpr uint64_t ERR = 64;
+#else
+constexpr uint64_t ERR = 128;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+// We choose the precision of the high part to be 53 - 24 - 8, so that when
+// y * (e_x + LOG2_R_DD[i].hi) is exact.
+// Generated by Sollya with:
+// > for i from 0 to 127 do {
+// r = 2^-8 * ceil(2^8 * (1 - 2^-8) / (1 + i * 2^-7) );
+// a = -log2(r);
+// b = round(1 + a, 53 - 24 - 8, RN) - 1;
+// c = round(a - b, D, RN);
+// d = round(a - b - c, D, RN);
+// print("{", d, ",", c, ", ", b, "},");
+// };
+static constexpr TripleDouble LOG2_R_TD[128] = {
+ {0.0, 0.0, 0.0},
+ {0x1.84a2c615b70adp-79, -0x1.177c23362928cp-25, 0x1.72c8p-7},
+ {-0x1.f27b820fd03eap-76, -0x1.179e0caa9c9abp-22, 0x1.744p-6},
+ {-0x1.f27ef487c8f34p-77, -0x1.c6cea541f5b7p-23, 0x1.184cp-5},
+ {-0x1.e3f80fbc71454p-76, -0x1.66c4d4e554434p-22, 0x1.773ap-5},
+ {-0x1.9f8ef14d5f6eep-79, -0x1.70700a00fdd55p-24, 0x1.d6ecp-5},
+ {0x1.452bbce7398c1p-77, 0x1.53002a4e86631p-23, 0x1.1bb3p-4},
+ {-0x1.990555535afdp-81, 0x1.fcd15f101c142p-25, 0x1.4c56p-4},
+ {0x1.447e30ad393eep-78, 0x1.25b3eed319cedp-22, 0x1.7d6p-4},
+ {0x1.b7759da88a2dap-76, -0x1.4195120d8486fp-22, 0x1.960dp-4},
+ {0x1.cee7766ece702p-78, 0x1.45b878e27d0d9p-23, 0x1.c7b5p-4},
+ {-0x1.a55c745ecdc2fp-77, 0x1.770744593a4cbp-22, 0x1.f9c9p-4},
+ {0x1.f7ec992caa67fp-77, 0x1.c673032495d24p-22, 0x1.097ep-3},
+ {-0x1.433638c6ece3ep-77, -0x1.1eaa65b49696ep-22, 0x1.22dbp-3},
+ {0x1.58f27b6518824p-76, 0x1.b2866f2850b22p-22, 0x1.3c6f8p-3},
+ {-0x1.86bdcfdfd4a4cp-79, 0x1.8ee37cd2ea9d3p-25, 0x1.494f8p-3},
+ {-0x1.ff7044a68a7fap-80, 0x1.7e86f9c2154fbp-24, 0x1.633a8p-3},
+ {-0x1.aa21694561327p-81, 0x1.8e3cfc25f0ce6p-26, 0x1.7046p-3},
+ {-0x1.d209f2d4239c6p-87, 0x1.57f7a64ccd537p-28, 0x1.8a898p-3},
+ {-0x1.a55e97e60e632p-76, -0x1.a761c09fbd2aep-22, 0x1.97c2p-3},
+ {0x1.261179225541ep-76, 0x1.24bea9a2c66f3p-22, 0x1.b26p-3},
+ {-0x1.08fa30510fca9p-82, -0x1.60002ccfe43f5p-25, 0x1.bfc68p-3},
+ {-0x1.63ec8d56242f9p-76, 0x1.69f220e97f22cp-22, 0x1.dac2p-3}...
[truncated]
``````````
</details>
https://github.com/llvm/llvm-project/pull/71188
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